Without context, it's impossible to be sure, but as socialism is a social/economic system/theory (i.e. not really something that can be allowed by law), I would say that most readers would understand "as allowed by law" to modify "discussed".
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Samuel LijinJul 3 '14 at 14:02

@SamuelLijin Not at all. As far back as the 1880s Bernard Shaw and the Fabians were very fond of pointing out that much of existing law was 'socialist' in intent and effect, and many contemporary conservatives echo that notion, albeit as a matter for outrage rather than approbation.
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StoneyBJul 3 '14 at 14:54

This question has implications beyond those which I think you intend to raise, so I have posted a further question about it on ELU
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StoneyBJul 3 '14 at 18:22

2 Answers
2

The phrase would be parsed as modifying discussed† only if it were set off with a comma (or expressed with corresponding comma-intonation in speech) or moved to an earlier position:

We discussed socialism, as allowed by law.

As allowed by law, we discussed socialism.

We discussed, as allowed by law, socialism. (*This one is grammatical but awkward with the very ‘light’ one-word direct object. The parenthetical as allowed by law seems to arise only as a mid-sentence afterthought.*)

In these cases the sentence would involve a “legally allowed discussion”.

But as you have written the sentence, without a comma, as allowed by law is understood to be a restrictive modifier on socialism: what we discussed might be expressed as “legally allowed socialism”.

† That is how traditional grammar would put it; contemporary grammars would more likely say that the phrase 'modifies' the entire clause.

It sounds like "as allowed by law" is modifying "discussed". As allowed by law is basically saying they discussed it as much as the law allowed them to, implying that the laws only allow them to talk about socialism to a certain extent.